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Let $H$ be a finite quasisimple classical group, i.e. $H$ is perfect and$S:=H/Z(H)$ is a finite simple classical group. We prove in this paper that,excluding the cases when the simple group $S$ has a very exceptional Schurmultiplier such as $\PSL_3(4)$ or $\PSU_4(3)$, $H$ is uniquely determined bythe structure of its complex group algebra. The proofs make essential use ofthe classification of finite simple groups as well as the results on primepower character degrees and relatively small character degrees of quasisimpleclassical groups.

Quasisimple classical groups and their complex group algebras